Hyperchaos-driven compressive image encryption framework with complete binary tree for enhanced security

Abstract Digital images are widely used in network communication. However, image transmission is vulnerable to unauthorized interception, which may cause serious privacy leakage. To address this problem, this paper proposes a secure image encryption algorithm that combines a hyperchaotic map, nonlinear bifurcation permutation, and block compressed sensing. First, a novel hyperchaotic map is designed. Its stability and complex chaotic behavior enable the generation of high-quality pseudo-random sequences for encryption keys. Second, block compressed sensing is introduced into the encryption process. This approach achieves simultaneous compression while reducing computational complexity. Third, a bit-level substitution mechanism based on a complete binary tree structure is constructed. This mechanism enables deep pixel-level replacement operations. Finally, a dual-feature diffusion mechanism is designed to further enhance security and robustness. Experimental results show that the proposed algorithm achieves strong encryption performance. It effectively resists various typical attacks. These results indicate that the algorithm is suitable for high-security applications, including medical image transmission and secure network communication.